Galoitica: Journal of Mathematical Structures and Applications

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https://doi.org/10.54216/GJSMA

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Galoitica: Journal of Mathematical Structures and Applications

Volume 10 , Issue 2 , PP: 19-26, 2024 | Cite this article as | XML | Html | PDF

A New Approach for Solving Singularly Perturbed Boundary Value Problems by Using Exponential Spline Method

Ahmed R. Khlefha 1 *

  • 1 Department of Mathematics, College of Education, University of Sumer, Thi-Qar, Iraq. - (arkdsh85@gmail.com)
  • Doi: https://doi.org/10.54216/GJMSA.0100202

    Received: October 19, 2023 Revised: January 16, 2024 Accepted: March 18, 2024
    Abstract

    This article presents the development of families of approaches for numerically solving singularly perturbed two-point boundary-value problems using exponential spline functions. The proposed approaches exhibit second-order and fourth-order accuracy and are suitable for both singular and non-singular problem scenarios. Numerical data are presented to demonstrate the efficacy of our methodologies and are compared with those proposed by various writers.

    Keywords :

    Exponential spline functions , boundary value problems, absolute errors , Convergence Analysis.

    References

     

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    [4]        Rashidinia J, Mohammadi R, Moatamedoshariati SH. Quintic spline methods for the solution of singularly perturbed boundary-value problems. International Journal for Computational Methods in Engineering Science and Mechanics 2010;11:247–57.

    [5]        Ranjan R, Prasad HS. A novel exponentially fitted finite difference method for a class of 2nd order singularly perturbed boundary value problems with a simple turning point exhibiting twin boundary layers. Journal of Ambient Intelligence and Humanized Computing 2022;13:4207–21.

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    [10]      Gebeyaw W, Andargie A, Adamu G. Solving second order singularly perturbed delay differential equations with layer behavior via initial value method. Journal of Applied Mathematics & Informatics 2018;36:331–48.

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    Cite This Article As :
    Ahmed R. Khlefha. "A New Approach for Solving Singularly Perturbed Boundary Value Problems by Using Exponential Spline Method." Full Length Article, Vol. 10, No. 2, 2024 ,PP. 19-26 (Doi   :  https://doi.org/10.54216/GJMSA.0100202)
    Ahmed R. Khlefha. (2024). A New Approach for Solving Singularly Perturbed Boundary Value Problems by Using Exponential Spline Method. Journal of , 10 ( 2 ), 19-26 (Doi   :  https://doi.org/10.54216/GJMSA.0100202)
    Ahmed R. Khlefha. "A New Approach for Solving Singularly Perturbed Boundary Value Problems by Using Exponential Spline Method." Journal of , 10 no. 2 (2024): 19-26 (Doi   :  https://doi.org/10.54216/GJMSA.0100202)
    Ahmed R. Khlefha. (2024). A New Approach for Solving Singularly Perturbed Boundary Value Problems by Using Exponential Spline Method. Journal of , 10 ( 2 ), 19-26 (Doi   :  https://doi.org/10.54216/GJMSA.0100202)
    Ahmed R. Khlefha. A New Approach for Solving Singularly Perturbed Boundary Value Problems by Using Exponential Spline Method. Journal of , (2024); 10 ( 2 ): 19-26 (Doi   :  https://doi.org/10.54216/GJMSA.0100202)
    Ahmed R. Khlefha, A New Approach for Solving Singularly Perturbed Boundary Value Problems by Using Exponential Spline Method, Journal of , Vol. 10 , No. 2 , (2024) : 19-26 (Doi   :  https://doi.org/10.54216/GJMSA.0100202)